A triangle DEF has DF=13 cm, angle EDF is equal to 37 degrees and angle DFE is equal to 68 degrees. The side length DE (to the nearest cm) is equal to

To solve this problem, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.

We know that DF = 13 cm, ∠EDF = 37 degrees, and ∠DFE = 68 degrees. We want to find the length of DE.

First, we can find ∠DEF by subtracting the other two angles from 180 degrees (since the sum of the angles in a triangle is 180 degrees):

∠DEF = 180 - 37 - 68 = 75 degrees

Now we can use the Law of Sines to find DE:

DE/sin(∠DEF) = DF/sin(∠DFE)

Plugging in the known values:

DE/sin(75) = 13/sin(68)

Solving for DE:

DE = (13/sin(68)) * sin(75)

Using a calculator to find the sine values and perform the calculation, we find that DE is approximately 13.6 cm. Rounding to the nearest cm, DE is approximately 14 cm.